Final answer:
The annual rate of interest on the $29,000 loan, taking into account the 20% compensating balance requirement and the treasurer's existing $2,400 chequing account balance, is approximately 14.62%, once adjusted for the effective loan amount.
Step-by-step explanation:
The annual rate of interest on the loan from Brandon Credit Union can be calculated by first determining the effective amount of the loan, given the compensating balance requirement. Since the treasurer keeps $2,400 in the firm's chequing account, this amount can be counted toward meeting the compensating balance requirement. To calculate the annual interest rate, we need to account for the effective loan amount after the compensating balance is factored in, and then convert the interest for the 180-day loan period to an annual rate.
The compensating balance required is 20% of the $29,000 loan, which amounts to $5,800. Since the treasurer already keeps $2,400 in the account, the additional compensating balance required is $5,800 - $2,400 = $3,400. Therefore, the effective loan amount is $29,000 - $3,400 = $25,600.
The interest for 180 days at a 12% annual rate on a $29,000 loan is calculated as follows:
Interest = Principal × Rate × Time = $29,000 × 0.12 × (180/365) = $1,815.89 (approximate)
However, because of the compensating balance, the borrower effectively receives only $25,600. Thus, to find the effective annual rate of interest, we calculate the following:
Effective Annual Interest Rate = (Interest / Effective Loan Amount) × (365 / Loan Period) × 100%
Effective Annual Interest Rate = ($1,815.89 / $25,600) × (365 / 180) × 100% = approximately 14.62%